Photo of Alastair Craw

Alastair Craw

Dr

  • 4 WEST 3.49

Accepting Doctoral Students

20022020

Research output per year

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Personal profile

Research interests

My research interests lie in pure mathematics, and specifically in algebraic geometry and representation theory. Much of my research applies explicit methods to improve our understanding of moduli spaces of quiver representations and their derived categories.

One motivating question is to ask for nice moduli descriptions of well known varieties. This is now understood for projective toric varieties and, more generally, for Mori Dream Spaces. This leads naturally to the study of multigraded linear series (also known as framed quiver varieties or quiver flag varieties) as ambient spaces in noncommutative algebraic geometry.Another theme of my research is to understand which algebraic varieties carry tilting bundles, thereby providing an explicit understanding of their derived category of coherent sheaves. The first known examples were provided by Beilinson and Kapranov, while many of the more recent examples have been influenced by the McKay correspondence in one form or another. Examples include framed quiver varieties, G-Hilbert schemes, moduli spaces arising in the study of consistent dimer model algebras, and smooth toric Fano varieties in low dimensions. These constructions lead to interesting questions about mutation, wall crossing phenomena and Bridgeland stability manifolds.

Education/Academic qualification

Mathematics, Doctor of Science, University of Warwick

Award Date: 12 Jul 2001

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Projects

  • Research Output

    Birational geometry of symplectic quotient singularities

    Bellamy, G. & Craw, A., 30 Apr 2020, In : Inventiones Mathematicae. 49 p.

    Research output: Contribution to journalArticle

    Open Access

    Combinatorial Reid's recipe for consistent dimer models

    Craw, A., Heuberger, L. & Tapia Amador, J., 2020, In : arXiv. 26 p.

    Research output: Contribution to journalArticle

    Punctual Hilbert schemes for Kleinian singularities as quiver varieties

    Craw, A., Gammelgaard, S., Gyenge, Á. & Szendrői, B., 29 Oct 2019, (Submitted) In : arXiv. 22 p.

    Research output: Contribution to journalArticle

    Multigraded linear series and recollement

    Craw, A., Ito, Y. & Karmazyn, J., 1 Jun 2018, In : Mathematische Zeitschrift. 289, 1-2, p. 535-565 31 p.

    Research output: Contribution to journalArticle

    Open Access
  • 2 Citations (Scopus)

    Reconstructing toric quiver flag varieties from a tilting bundle

    Craw, A. & Green, J., 1 Mar 2018, In : European Journal of Mathematics. 4, 1, p. 185–199 15 p.

    Research output: Contribution to journalArticle

    Open Access
  • Thesis

    Combinatorial Reid's Recipe for Consistent Dimer Models

    Author: Tapia Amador, J., 30 Jun 2015

    Supervisor: Craw, A. (Supervisor)

    Student thesis: Doctoral ThesisPhD

    File

    Non-singular actions of countable groups

    Author: Jarrett, K., 14 Aug 2018

    Supervisor: Dooley, A. (Supervisor), Craw, A. (Advisor) & Fischer, V. (Advisor)

    Student thesis: Doctoral ThesisPhD

    File

    Reconstructing certain quiver flag varieties from a tilting bundle

    Author: Green, J., 22 Nov 2018

    Supervisor: Craw, A. (Supervisor) & Calderbank, D. (Supervisor)

    Student thesis: Doctoral ThesisPhD

    File

    Tilting Bundles and Toric Fano Varieties

    Author: Prabhu-Naik, N., 3 Nov 2015

    Supervisor: Craw, A. (Supervisor)

    Student thesis: Doctoral ThesisPhD

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